Approximative properties of mixed series by Lagerre's polynomials onclasses of smooth functions

Approximative properties of mixed series by Lagerre's polynomials on classes of smooth functions that given on axle $[0,\infty)$ are viewed. Inequality that corresponds to Lebesgue inequality for trigonometric Fourier sumswas found for evaluation of deflection of smooth function from it's partial sums of mixed series by Lagerre's polynomials. Evaluations for corresponding Lebesgue function of partial sums of mixed series by Lagerre's polynomials were found.